(a) FIELD OF THE INVENTION
The present invention relates to a gain-controlled amplifier whose gain varies exponentially in response to a linear voltage variation of a control voltage applied to the amplifier.
(b) DESCRIPTION OF THE PRIOR ART
FIG. 1 shows one conventional gain-controlled amplifier of the type in which bipolar transistors of different conduction type are utilized. In FIG. 1, reference numeral 1 denotes a bipolar transistor pair which comprises two PNP transistors, reference numeral 2 denotes a transistor pair which comprises two NPN transistors, and 3 and 4 denote operational amplifiers, respectively. The gain of the amplifier shown in FIG. 1 varies exponentially in response to a linear voltage variation of a control voltage Vc applied to the amplifier. The principle of operation of the above-described amplifier will be described.
With the arrangement of the circuit of the amplifier, the following equations are obtained: EQU i.sub.i =Vi/Ri (1a) EQU io=Vo/Ro (1b) EQU i.sub.i +i.sub.1 =i.sub.4 ( 1c) EQU i.sub.2 =io+i.sub.3 ( 1d) EQU V.sub.2 =V.sub.1 -VB (1e)
From the characteristics of p-n junction of semiconductor, the following equations are obtained when a saturation current of each p-n junction is expressed as i.sub.s : EQU i.sub.1 =i.sub.s .multidot.exp {(q/kT).multidot.V.sub.1 } (2a) EQU i.sub.2 =i.sub.s .multidot.exp {(q/kT).multidot.(V.sub.1 -Vc) (2b) EQU i.sub.3 =i.sub.s .multidot.exp {(q/kT).multidot.V.sub.2 } (2c) EQU i.sub.4 =i.sub.s .multidot.exp {(q/kT).multidot.(V.sub.2 +Vc) (2d)
where,
q: an electric charge of an electron PA1 k: Boltzmann's constant PA1 T: the junction temperature in absolute temperature.
A voltage gain Vo/Vi of this amplifier is obtained by simplifying the above mentioned equations as follows: EQU Vo/Vi=(-Ro/Ri) exp {(q/kT).multidot.Vc} (3)
It will be understood from the equation (3) that the voltage gain varies exponentially in response to a linear voltage variation of the control voltage Vc applied to the amplifier.
However, the gain-controlled amplifier shown in FIG. 1 has a problem that the distortion generated therein is large because the amplifier utilizes the transistor pairs of different conduction types and the characteristics of the PNP transistors and NPN transistors are different from each other.
To solve the above-mentioned problem, an amplifier which utilizes transistor pairs of the same conduction type has been developed.
FIG. 2 shows the circuit of one of such gain-controlled amplifiers.
In FIG. 2, reference numerals 6 and 7 denote input terminals to which input signals (Vi and -Vi) opposite in phase to each other are applied, and those input terminals 6 and 7 are connected to inverting input terminals of operational amplifiers 10 and 11 through resistors 8 and 9 (values are both Ri), respectively. Reference numeral 12 denotes a transistor pair which comprises NPN transistors 12a and 12b of which emitters are connected to each other. Similarly, reference numeral 13 denotes a transistor pair which comprises NPN transistors 13a and 13b of which emitters are connected to each other. And, the common emitters of both transistor pairs 12 and 13 are connected to output terminals of the operational amplifiers 10 and 11, respectively. A collector of the transistor 12a is connected to an output terminal of a constant current supply 14 (value is IB) and the inverting input terminal of the operational amplifier 10, and the base of the transistor 12a is connected to the ground. A collector of the transistor 13a is connected to an output terminal of a constant current supply 15 (value is IB) and the inverting input terminal of the operational amplifier 11, and the base of the transistor 13a is connected to the ground. Reference numeral 16 denotes a variable voltage supply for outputting a control voltage Vc, and the control voltage Vc is supplied to bases of the transistors 12b and 13b. Reference numeral 17 denotes a current-to-voltage converter which comprises a resistor 18 (value is RL) and an operational amplifire 19, and reference numeral 20 denotes a circuit of a current-to-voltage converter which comprises a resistor 21 (value is RL) and an operational amplifier 22. The current-to-voltage converters 17 and 20 convert collector currents of the transistors 12b and 13b to voltage signals. Reference numeral 25 denotes a subtraction circuit which comprises resistors 26 to 29 (values are all R) and an operational amplifier 30. The subtraction circuit 25 subtracts the output signal of the current-to-voltage converter 17 from that of the current-to-voltage converter 20, and outputs the subtraction result as an output signal Vo.
The operation of the above-mentioned circuit will now be explained. With the arrangement of the circuit, when currents i.sub.1 to i.sub.4 flow as shown in FIG. 2, the following equations are obtained from the characteristics of the P-N junction: EQU i.sub.1 =Vi/Ri+IB (4a) EQU i.sub.2 =i.sub.1 .multidot.exp (K.multidot.Vc) (4b) EQU i.sub.3 =IB-Vi/Ri (4c) EQU i.sub.4 =i.sub.3 .multidot.exp (K.multidot.Vc) (4d)
where, K=q/kT.
On the other hand, the output voltage V.sub.0 of the circuit can be expressed by the following equation: EQU Vo=i.sub.4 .multidot.RL-i.sub.2 .multidot.RL (5)
And therefore, the output voltage Vo can be expressed by the following equation by substituting the above-mentioned equations (4a) to (4d) for this equation (5) EQU Vo=i.sub.3 .multidot.exp (K.multidot.Vc)-i.sub.1 .multidot.exp (K.multidot.Vc)=(-2Vi/Ri).multidot.exp (K.multidot.Vc) (6)
The voltage gain (Vo/Vi) of the circuit shown in FIG. 2 is obtained by transforming the equation (6) as follows: EQU (Vo/Vi{=(-2/Ri).multidot.exp (K.multidot.Vc) (7)
This equation (7) shows that the voltage gain is controlled by the control voltage Vc in the above-mentioned circuit.
However, the circuit shown in FIG. 2 has a deficiency as described hereunder.
A bias voltage Va at a point a in the circuit shown in FIG. 2 will first be examined. When the input signal Vi is 0, the current i.sub.2 is expressed as follows from the above-mentioned equations (4a) and (4b): EQU i.sub.2 =IB.multidot.exp (K.multidot.Vc) (8)
Therefore, the voltage Va at the point a can be expressed by the following equation (9): EQU Va=i.sub.2 .multidot.RL=IB.multidot.exp (K.multidot.Vc).multidot.RL (9)
A voltage Vb at a point b in the above-mentioned circuit can be also obtained in a manner described above for the voltage Va and is expressed by the following equation: EQU Va=IB.multidot.exp (K.multidot.Vc).multidot.RL (10)
It will be understood from the above equations (9) and (10) that the biases at the point a and the point b depend on the control voltage Vc. When the control voltage Vc is made larger to render the gain larger in the conventional gain-controlled circuit shown in FIG. 2, the potentials at the point a and the point b increase, so that the operational amplifiers 19 and 22 are liable to saturate. Therefore, in such condition, the dynamic range of the amplifier becomes smaller, so that the maximum amplitude of the input signal Vi is limited significantly.
The conventional gain-controlled amplifier shown in FIG. 2, thus has a reduced distortion due to the utilization of the transistor pairs of the same conduction-type transistors, but, on the other hand, the amplifier has a deficiency that the dynamic range thereof becomes smaller when the control voltage Vc is made greater to render the gain higher.